In the context of trigonometry, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
For an angle of 30 degrees, we can determine its sine value from basic trigonometric principles. Specifically, sin 30° is a well-known value that is equal to 0.5. This means that in any right triangle where one of the angles measures 30 degrees, the length of the side opposite that angle is half the length of the hypotenuse.
This relationship can be visualized using a special right triangle known as a 30-60-90 triangle, where the sides are in the ratio 1:√3:2. In this triangle, the side opposite the 30° angle is 1, and the hypotenuse is 2, confirming that:
sin 30° = (length of opposite side) / (length of hypotenuse) = 1/2 = 0.5
Therefore, in triangle QRS, if one of the angles is 30°, then sin 30° is equal to 0.5.